Due to a lack of both motivation (owing to broken hardware) and time (owing to life), I haven't worked on the watch since the last project log 11 days ago. However, in that time, I did leave the board connected to the battery (albeit without a screen). On a whim today, I measured the voltage across the battery, and I got a surprising 3.9 volts. The "full" voltage is 4.2V, and LiPo batteries don't discharge linearly. In fact, based on this chart from Adafruit, I've lost less than 20% of the battery in the last 11 days:

There's no screen connected, no backlight use, and no Bluetooth communications, so this result doesn't really represent a real-life test. However, it does confirm that my estimates of multiple weeks on a single charge weren't completely ridiculous. 

It's not all good news, though. When I plugged in my test display (the one that doesn't fit in the case), it had tons of display artifacts that made it unreadable. These cleared up immediately as soon as I connected USB power, which leads me to believe that I do actually need that 5V boost converter after all. I suppose I've got nothing but time to add it...